Production Control in a Competitive Environment with Incomplete Information

  • Konstantin KoganEmail author
  • Fouad El Ouardighi
Part of the AIRO Springer Series book series (AIROSS, volume 1)


We consider an industry consisting of a large number of firms producing substitutable products and engaged in a dynamic Cournot-type competition. The firms are able to reduce their marginal production costs by accumulating their own experience as well as the experience spillovers from other firms. In particular, firms accumulate production experience through proprietary learning, which, however, depreciates over time. We determine steady-state Nash equilibrium policies that are based on the assumption that the firms do not have precise information about each competitor and therefore are unable to respond to a specific firm’s dynamics. The firms, however, do react to overall industry trends. We show that in such a case, though the information used for production control is incomplete, in the long run the firms tend to the output they would converge to under complete information. We also find that industry growth due to more firms entering the market results in decreasing long-run equilibrium output of each firm when the depreciation of experience is higher than the rate of spillovers. Otherwise, the opposite result can emerge, i.e., the steady-state output will grow.


Production Control Differential games Quantity competition 


  1. 1.
    Arrow, K.J.: The economic implications of learning by doing. Rev. Econ. Stud. 29(3), 155–173 (1962)CrossRefGoogle Scholar
  2. 2.
    Cellini, R., Lambertini, L.: Dynamic R&D with spillovers: competition vs cooperation. J. Econ. Dyn. Control 33(3), 568–582 (2009)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Cohn, D., Tesauro, G.: How tight are the Vapnik-Chervonenkis bounds? Neural Comput. 4(2), 249–269 (1992)CrossRefGoogle Scholar
  4. 4.
    Cournot, A.A.: Researches into the Mathematical Principles of the Theory of Wealth. Augustus M. Kelley Publishers, New York, 1971 (1838)Google Scholar
  5. 5.
    Dutton, J.M., Thomas, A.: Treating progress functions as a managerial opportunity. Acad. Manag. Rev. 9(2), 235–247 (1984)CrossRefGoogle Scholar
  6. 6.
    Fudenberg, D., Tirole, J.: Learning by doing and market performance. Bell J. Econ. 14, 522–530 (1983)CrossRefGoogle Scholar
  7. 7.
    Jarmin R.S.: Learning by doing and competition in the early rayon industry. CES, 93–4 (1993)Google Scholar
  8. 8.
    Jørgensen, S., Zaccour, G.: Optimal output strategies in a two-stage game with entry, learning-by-doing and spillovers. In: Petrosjan, A., Mazalov, V.V. (eds.) Game Theory and Applications. Nova Science Publishers, New York (2000)zbMATHGoogle Scholar
  9. 9.
    Kogan, K., El Ouardighi, F., Herbon, A.: Production with learning and forgetting in a competitive environment. Int. J. Prod. Econ. (IJPE). 189, 52–62 (2017)CrossRefGoogle Scholar
  10. 10.
    Miravete, E.J.: Time-consistent protection with learning by doing. Eur. Econ. Rev. 47(5), 761–790 (2003)CrossRefGoogle Scholar
  11. 11.
    Schroeder, M.: Fractals, Chaos, Power Laws: minutes From An Infinite Paradise. Freeman, New York (1991)zbMATHGoogle Scholar
  12. 12.
    Spence, A.M.: The learning curve and competition. Bell J. Econ. 12(Spring), 49–70 (1981)CrossRefGoogle Scholar
  13. 13.
    Stokey, N.L.: The dynamics of industry-wide learning. In: Heller, W.P., Starr, R.M., Starrett, D.A. (eds.). Essays in Honor of Kenneth J. Arrow, vol. 2. Cambridge, Cambridge University PressGoogle Scholar
  14. 14.
    Yelle, L.E.: The learning curve: historical review and comprehensive survey. Decis. Sci. 10(2), 302–328 (1979)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Management DepartmentBar-Ilan UniversityRamat-GanIsrael
  2. 2.Operations Management DepartmentESSEC Business SchoolCergy PontoiseFrance

Personalised recommendations